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The RAON accelerator is currently under construction to generate and accelerate stable ions and rare isotopes for various kinds of scientific programs, and it will be completed by the end of 2021. In the RAON accelerator, the beams generated by using ion sources such as electron cyclotron resonance ion source and isotope separation on-line can be used in high energy experiments such as a beam irradiation system and a muon spin rotation/relaxation/resonance system after having been accelerated by low energy and high energy superconducting linacs. After the high energy superconducting linac, the beam passes through the high energy beamline and then collides with the target. In 2015, the lattices of the high energy beamlines were designed achromatically to minimize the emittance growth. However, as the specification of magnets in the beamline was changed after first lattice design, a beam dynamics simulation has been performed newly, and beam loss studies have also been conducted. Here, we will present the simulation results for the beam dynamics and describe the beam loss studies performed on the high energy beamlines of the RAON accelerator.

As the beam intensity increases in modern high-power accelerators, self-field effects of the beam become significant and it is the utmost goal to minimize the beam loss of halo particles by avoiding or minimizing contributions of various halo mechanisms. There are two distinct families of space-charge halo mechanisms in high-intensity linear accelerators, and yet they need to be differentiated: resonances (single particle resonances or incoherent resonances) and instabilities (parametric resonances or coherent resonances). What we call resonances are resonances of the beam particle excited through the space-charge nonlinear multipoles. What we call instabilities (or envelope instabilities) are instabilities of the beam envelope. Instabilities are also called parametric resonances because they are parametric resonances of the envelope equation. They would better be called envelope parametric resonances to distinguish them from particle parametric resonances. Resonances and instabilities may look alike in the phase space, and yet they have distinct differences. Instabilities (or envelope parametric resonances) do not have the resonant frequency component. Various orders of resonances and instabilities are presented along with the beam distributions with which the particular mechanism is observed.

Studies of the machine imperfections in the RAON superconducting linac (SCL) that employs normal conducting (NC) quadrupoles were done to assess the tolerable error budgets of the machine imperfections that ensure operation of the beam. The studies show that the beam loss requirement is met even before the orbit correction and that the beam loss requirement is met even without the MHB (multi-harmonic buncher) and VE (velocity equalizer) thanks to the RAON’s radio-frequency quadrupole (RFQ) design feature. For the low energy section of the linac (SCL3), a comparison is made between the two superconducting linac lattice types: one lattice that employs NC quadrupoles and the other that employs SC solenoids. The studies show that both lattices meet the beam loss requirement after the orbit correction. However, before the orbit correction, the lattice employing SC solenoids does not meet the beam loss requirement and can cause a significant beam loss, while the lattice employing NC quadrupoles meets the requirement. For the lattice employing SC solenoids, care must be taken during the beam commissioning.

For modern high-intensity linear accelerators , the well-known envelope instability and recently reported fourth-order particle resonance impose a fundamental operational limit (i.e., zero-current phase advance should be less than 90 ° ). Motivated by the stability of spinning flying objects, we propose a novel approach of using spinning beams to surpass this limit. We discovered that spinning beams have an intrinsic characteristic that can suppress the impact of the fourth-order resonance on emittance growth and the associated envelope instability.

The Rare Isotope Accelerator of Newness (RAON) accelerator is under construction to generate and accelerate the stable ion beams and the rare isotope beams for various kinds of experiment programs. Especially, the post accelerator section was designed to be able to separately accelerate and transport the stable ion beams created by the superconducting electron cyclotron resonance ion source (ECR-IS) and the rare isotope beams created by the Isotope Separation On-Line (ISOL) system. However, recently, the research of the simultaneous operation of the stable ion beams and the rare isotope beams has been conducted to more efficiently satisfy the a wide range of beam requirements of the experimental halls. For the operation, we has modified the lattice of the post low energy beam transport (LEBT) section for the injection of the rare isotope beam and the next lattice after the low energy superconducting linac (SCL3) section for the extraction of the accelerated beam in the post accelerator section of the RAON accelerator. In this paper, the new lattice designs of the injection and extraction parts will be presented and we will describe the results of the beam dynamics simulations for the simultaneous operation of the two kinds of beams.

The RAON accelerator has been built to create and accelerate stable heavy-ion beams and rare isotope beams. The stable heavy-ion beams are generated by the superconducting electron cyclotron resonance ion source and accelerated by the low energy superconducting linac SCL1. The beams accelerated by the SCL1 are re-accelerated by the high energy superconducting linac SCL2 for the generation of rare isotope beams by using the in-flight fragmentation system or are put to use in the low energy experimental halls, which include the neutron science facility and the KOrea Broad acceptance Recoil spectrometer and Apparatus after having passed through the low energy beam lines which have long deflecting sections. At the end of each beam line in the low energy experimental halls, the beams should meet the targets of the two facilities with the specific requirements satisfied. Namely, if the beam is to be sent safely and accurately to the targets and simultaneously, satisfy the requirements, an achromatic lattice design needs to be applied in each beam line. In this paper, we will present the lattice design of the low energy beam lines and describe the results of the beam dynamics simulations. In addition, the correction of the beam orbit, which is distorted by machine imperfections, will be discussed.

The driver accelerator of the RAON is a superconducting linear accelerator consisting of low beta cavities. Studies of various failure modes are performed through extensive machine imperfection studies. It is found that the linac is tolerant of any single superconducting cavity loss except the first nine upstream QWR cavities. Studies also find that the linac design is tolerant of 10% upstream-section cavity failure with the design-beta cavities. It is also found that in case of 10% cavity failure, orbit correction becomes indispensable. On the other hand, if cavity betas of the HWR and the SSR2 increase by 4% from the design values, the linac beam loss starts to increase rapidly, when 10% upstream-section cavities become inoperable. This paper shows quantitatively that significant beam losses can be caused in case of cavity faults, when the exit energy of the upstream section is not high enough. In case of a quadrupole doublet failure in the QWR section, beam loss of about 70 W/m is generated in the immediate downstream and beam operation is not feasible.

Since the finding of the space charge fourth order 4σ=360° resonance [Jeon et al., 2009 [3]], studies have been carried out to better understand the fourth order resonance and the envelope instability in high intensity linear accelerators. The questions remained unanswered under what conditions the envelope instability is excited or suppressed following the development of the fourth order resonance. Simulations suggest that the variation of σo and σ along the linac, the halo particles and the resonance islands of the fourth order resonance play an important role in exciting or suppressing the envelope instability after the fourth order resonance is manifested for initially well-matched beams. Here σ(σo) is the depressed (zero-current) phase advance per cell. The envelope instability is excited from the mismatch generated by the fourth order resonance, 1) when σo is maintained approximately constant or increases along the linac with σo>90° and 2) when the extent of the fourth order resonance shrinks, as σ increases approaching 90°. On the other hand, when σ stays almost constant (maintaining the fourth order resonance) or when σo decreases and gets close to 90° (getting out of the envelope instability), the envelope instability is suppressed and the halo particles formed by the fourth order resonance preserves a four-fold structure in the phase space.

We investigated optimum choices of accelerator parameters for superconducting-technology-based heavy-ion linear accelerator (linac) to achieve the high beam quality at an in-flight target with a high beam power of 400 kW. The superconducting linac system is designed to provide a stable-ion beams from protons to uranium with energies of 600 MeV and 200 MeV/u, respectively. The linac optics is also designed such that the effects of envelope instability, parametric resonance between the transverse and longitudinal planes, beam steering effect due to asymmetric field in quarter-wave resonance (QWR) cavities, and emittance growth in charge strippers due to the straggling effect, parametric resonance, and envelope instability become as small as possible. The dimensions of the warm and cold sections in the low-energy section which mainly determine the longitudinal acceptance of the linac are optimized to achieve a longitudinal acceptance larger than 27 keV/u-ns enabling stable operation. The tracking simulation for the uranium beam was performed and we achieved the transverse normalized rms emittance of 0.095 mm-mrad and longitudinal rms emittance of 2.10 keV/u-ns at the end of designed linac without uncontrolled beam losses along the linac. In order to estimate the degradation of the machine performance due to imperfections such as misalignment, ripple of the magnet power source, and phase and power variation of the RF source, the particle tracking simulation was performed and the uncontrolled beam loss with the machine imperfection without the orbit and optics correction was less than 1 W/m which is a condition required for machine operation. The optimum scheme for orbit correction in the low-energy linac is investigated based on the transfer matrix of the elements and the validation of the scheme is confirmed by the particle tracking simulation using TRACK code.

In RAON heavy ion accelerator, beams generated by superconducting electron cyclotron resonance ion source (ECR-IS) or Isotope Separation On-Line (ISOL) system are accelerated by lower energy superconducting linac and high energy superconducting linac. The accelerated beams are used in the high energy experimental hall which includes bio-medical and muon-SR facilities, after passing through the high energy beam transport lines. At the targets of those two facilities, the stable and small beams meeting the requirements rigorously are required in the transverse plane. Therefore the beams must be safely sent to the targets and simultaneously satisfy the two requirements, the achromatic condition and the mid-plane symmetric condition, of the targets. For this reason, the lattice design of the high energy beam transport lines in which the long deflecting sections are included is considered as a significant issue in the RAON accelerator. In this paper, we will describe the calculated beam optics satisfying the conditions and present the result of particle tracking simulations with the designed lattice of the high energy beam transport lines in the RAON accelerator. Also, the orbit distortion caused by the machine imperfections and the orbit correction with correctors will be discussed.

RAON has been designed as a rare isotope accelerator facility for the Rare Isotope Science Project (RISP). The main accelerator for the in-flight system accelerates uranium and proton beams to 200 MeV/u and 660 MeV, respectively, with a beam power of 400 kW. The front-end system consists of two 28 GHz electron cyclotron resonance ion sources (10 keV/u), a low-energy beam transport (LEBT) line with two 90° bends, a multi-harmonic buncher with three different rf frequencies, a radio-frequency quadrupole (RFQ), and a medium-energy beam transport line (MEBT) with three rebunchers and eight quadrupoles. A driver linac system consisting of Linac-1 and Linac-2 has been designed to optimize the beam and accelerator parameters so as to meet the required design goals. A charge stripper section is located between Linac-1 and Linac-2. To optimize these designs, we performed start-to-end simulations with the beams from the LEBT to Linac-2 using 1 million macroparticles. We present the resulting beam dynamics to evaluate the performance of the accelerator. Our simulation results predict that the transmission rate of the uranium beam is 85.8% from the LEBT to Linac-2. The designed facility is expected to achieve the required beam loss condition of less than 1 W/m. The RAON driver linac lattice design was developed and an overview of the beam dynamics is presented.

In RAON heavy ion accelerator, generally, the In-flight Fragmentation (IF) and Isotope Separation On-Line (ISOL) systems are employed in order to produce various isotope beams. Out of the isotope beams, the beams generated by the ISOL system are transported from the low energy linac SCL3 to the high energy driver linac SCL2. The post-accelerator to the driver linac transport (P2DT) section that consists of the charge stripper section, the 180° bending section, and the SCL2 matching section is placed between the SCL3 and the SCL2. In this P2DT section, however, the transverse and longitudinal emittance growth can aggravate the beam acceptance of the SCL2. Besides, the growth at the P2DT 180° bending section is considered a significant issue because of the unexpected achromatic effect. Therefore an achromatic and isochronous lattice design should be devised to prevent the transverse and longitudinal emittance from increasing while the multi-charge beams flow through the bending section. This study reports an improved design for the achromatic and isochronous lattice up to the second-order. After satisfying the first-order achromatic and isochronous condition by adjusting the field strength of quadrupoles with this design, the simple and efficient method will be utilized with the aim of getting the minimum number of sextupoles. The research on the collimator for the charge selection at the bending section will be also represented by using the designed lattice.

The driver linac of the heavy ion accelerator called RAON will be built in Korea and it utilizes four types of superconducting cavities. The SCL1 (Superconducting Linac 1) consists of the QWR (Quarter Wave Resonator, β=0.047, 81.25 MHz) cavities and the HWR (Half Wave Regenerator, β=0.21, 162.5 MHz) cavities. The SCL2 (Superconducting Linac 2) consists of the SSR1 (Single Spoke Resonator1, β=0.3, 325 MHz) and the SSR2 (β=0.51, 325 MHz) cavities. The manufacturing of the prototypes of the SSR1 and SSR2 cryomodules is on-going and the current status is reported. The issues included are the estimation of the thermal load, the P&ID of the cryomodules, as well as the results of the thermal and structural designs of the cryomodule components such as the two phase pipe, support posts and flow pipes.

The charge stripping section of the Rare isotope Accelerator Of Newness (RAON), which is one of the critical components to achieve a high power of 400 kW with a short lianc, is a source of transverse emittance growth. The dominant effects are the angular straggling in the charge stripper required to increase the charge state of the beam and chromatic aberrations in the dispersive section required to separate the selected ion beam from the various ion beams produced in the stripper. Since the main source of transverse emittance growth in the stripper is the angular straggling, it can be compensated for by changing the angle of the phase ellipse. Therefore the emittance growth is minimized by optimizing the Twiss parameters at the stripper. The emittance growth in the charge selection section is also minimized by the correction of high-order aberrations using six sextupole magnets. In this paper, we present a method to minimize the transverse emittance growth in the stripper by changing the Twiss parameters and in the charge selection section by using sextupole magnets.

Properties of the thermal radiation from arbitrary fractional dimension are investigated. Generalized blackbody radiation for arbitrary dimension can be obtained and the energy density is shown as a function of arbitrary dimension as well as temperature. Maximum frequency factor representing the relation between most probable photon energy and thermal energy is shown as a function of arbitrary fractional dimension. It is also shown how to measure the arbitrary fractional dimension of the body with thermal radiation.

The main aim of the Rare Isotope Science Project is to construct a high power heavy-ion accelerator based on the superconducting linear accelerator (SCL). The heavy ion accelerator is a key research facility that will allow ground-breaking research into numerous facets of basic science, such as nuclear physics, astrophysics, atomic physics, life science, medicine and material science. The machine will provide a beam power of 400 kW with a 238U79+ beam of 8 pμA and 200 MeV/u. One of the critical components in the SCL is the charge stripper between the two segments, SCL1 and SCL2, of the SCL. The charge stripper removes electrons from the ion beams to enhance the acceleration efficiency in the subsequent SCL2. To improve the efficiency of acceleration and power in SCL2, the optimal energy of stripped ions in a solid carbon foil stripper was estimated using the code LISE++. The thickness of the solid carbon foil was 300 μg/m2. The charge stripping efficiency of the solid carbon stripper in the present study was approximately 87%. For charge selection from the ions produced by the solid carbon stripper, a dispersive section is needed down-stream of the foil. The designed optics for the dispersive section is based on the mirror-symmetric optics to minimize the effect of high-order aberrations.

The Rare Isotope Science Project (RISP) was launched by the Institute for Basic Science (IBS) in December 2011 in Korea. The project aims to construct the new accelerator complex consisting of the Isotope Separation On-Line (ISOL) and the In-Flight Fragment (IF) facilities for the rare isotope science. The scientific programs and the experimental systems of RISP are briefly introduced with an overview of the complex.

The injector for the main driver linac of the Rare Isotope Science Project (RISP) in Korea has been designed to supply ions ranging from proton to uranium which will be used to meet requirements of the 400 kW inflight fragmentation (IF) system. The injector includes two superconducting electron cyclotron resonance (ECR) ion sources, a low energy beam transport (LEBT), a radio frequency quadrupole (RFQ), and a medium energy beam transport (MEBT). Major elements were optimized and selected by calculating uranium beam optics which will then be delivered to the low energy superconducting linac.

See paper for full list of authors; The Korea Rare Isotope Accelerator, currently referred to as KoRIA, is briefly presented. The KoRIA facility is aimed to enable cutting-edge sciences in a wide range of fields. It consists of a 70 kW isotope separator on-line (ISOL) facility driven by a 70 MeV, 1 mA proton cyclotron and a 400 kW in-flight fragmentation (IFF) facility. The ISOL facility uses a superconducting (SC) linac for post-acceleration of rare isotopes up to about 18 MeV/u, while the SC linac of IFF facility is capable of accelerating uranium beams up to 200 MeV/u, 8 pμA and proton beams up to 600 MeV, 660 μA. Overall features of the KoRIA facility are presented with a focus on the accelerator design.

It is important to accomplish adequate matching for a high intensity linear accelerator such as the SNS linac to minimize the mismatch and potential beam loss. In the early stage of the SNS linac design, there was a discussion over whether to match the core or to match the tail. The present study shows that the matching by minimizing rms emittances reduces both the core emittance and the beam tail, providing a stable and unambiguous matching for the SNS Drift Tube Linac, when an emittance scanner is available. For the transverse matching of other sections of the SNS linac where only wire-scanners are available, we use beam size data obtained from multiple wire-scanners installed in series to do the matching with the help of an envelope code such as Trace3D. It is verified that matching is improved through the matching technique based on the beam profile measurements from wire-scanners in series.

When a beam passes through superconducting cavities, it excites beam induced fields in the cavities. A systematic study is performed to study the beam loading effects with β

For high intensity proton accelerators, it is vital to reduce the machine activation by minimizing the beam loss from many sources. One of such sources is longitudinal mismatch. To minimize a potential mismatch, it is important to set accurately the rf set-point (rf field amplitude and phase) of a high-intensity linac such as the drift tube linac (DTL) of the spallation neutron source. A widely used technique called the acceptance scan was studied extensively and applied successfully to tune the DTL tanks since the initial commissioning. From the acceptance scan one can obtain the longitudinal beam profile at the entrance of each DTL tank. But except tank 1, acceptance scan alone cannot determine the incoming beam energy deviation, leading to small uncertainties in the rf set point.

The Spallation Neutron Source (SNS) accelerator delivers a one mega-Watt beam to a mercury target to produce neutrons used for neutron scattering materials research. It delivers ~ 1 GeV protons in short (< 1 us) pulses at 60 Hz. At an average power of ~ one mega-Watt, it is the highest-powered pulsed proton accelerator. The accelerator includes the first use of superconducting RF acceleration for a pulsed protons at this energy. The storage ring used to create the short time structure has record peak particle per pulse intensity. Beam commissioning took place in a staged manner during the construction phase of SNS. After the construction, neutron production operations began within a few months, and one mega-Watt operation was achieved within three years. The methods used to commission the beam and the experiences during initial operation are discussed.

It is shown that the sixth-order 6σ=720° (or 6∶2) resonance is manifested for high-intensity beams of linear accelerators through the space charge potential when the depressed phase advance per cell σ is close to and below 120° but no resonance effect is observed for σ above 120°. Simulation studies show a clear emittance growth by this resonance and a characteristic sixfold resonance structure in phase space. To verify that this is a resonance, a frequency analysis was conducted and a study was performed of crossing the resonance from above and from below the resonance. Canonical perturbation is carried out to show that this resonance arises through perturbation of strong 2σ=360° (2∶1) and 4σ=360° (4∶1) space charge resonances. Simulations also show that the space charge 6σ=360° (or 6∶1) resonance is very weak.

Beam instabilities due to High Order Modes (HOMs) are a concern to superconducting (SC) linacs such as the Spallation Neutron Source (SNS) linac. The effects of pulsed mode operation on transverse and longitudinal beam breakup instability are studied for H− beam in a consistent manner for the first time. Numerical simulation indicates that cumulative transverse beam breakup instabilities are not a concern in the SNS SC linac, primarily due to the heavy mass of H− beam and the HOM frequency spread resulting from manufacturing tolerances. As little as ±0.1 MHz HOM frequency spread stabilizes all the instabilities from both transverse HOMs, and also acts to stabilize the longitudinal HOMs. Such an assumed frequency spread of ±0.1 MHz HOM is small, and hence conservative compared with measured values of σ=0.00109(fHOM−f0)/f0 obtained from Cornell and the Jefferson Lab Free Electron Laser cavities. However, a few cavities may hit resonance lines and generate a high heat load. It is therefore prudent to have HOM dampers to avoid the danger of quenching a cavity.

In linacs for intense pulsed proton accelerators, the beam has a multiple time-structure, and each beam time-structure generates resonance. When a higher-order mode (HOM) is near these resonance frequencies, the induced voltage could be large and accordingly the resulting HOM power, too. In order to understand the effects of a complex beam time-structure on the mode excitations and the resulting HOM powers in elliptical superconducting cavities, analytic expressions are developed, with which the beam-induced voltage and corresponding power are explored, taking into account the properties of HOM frequency behavior in elliptical superconducting cavities. The results and understandings from this analysis are presented with the beam parameters of the Spallation Neutron Source (SNS) superconducting linac.

For the 4σ = 360° space-charge resonance in high intensity linear accelerators, the emittance growth is surveyed for input Gaussian beams, as a function of the depressed phase advance per cell σ and the initial tune depression (σo – σ). For each data point, the linac lattice is designed such that the fourth order resonance dominates over the envelope instability. The data show that the maximum emittance growth takes place at σ ≈ 87° over a wide range of the tune depression (or beam current), which confirms that the relevant parameter for the emittance growth is σ and that for the bandwidth is σo – σ. An interesting four-fold phase space structure is observed that cannot be explained with the fourth order resonance terms alone. Analysis attributes this effect to a small negative sixth order detuning term as the beam is redistributed by the resonance. Analytical studies show that the tune increases monotonically for the Gaussian beam which prevents the resonance for σ > 90°. Frequency analysis indicates that the four-fold structure observed for input Kapchinskij-Vladmirskij beams when σ

A new type of spin depolarization resonance has been observed at the Brookhaven Alternating Gradient Synchrotron (AGS). This spin resonance is identified as a strong closed-orbit sideband around the dominant intrinsic spin resonance. The strength of the resonance was proportional to the 9th harmonic component of the horizontal closed orbit and proportional to the vertical betatron oscillation amplitude. This ''hybrid'' spin resonance cannot be overcome by the partial snake at the AGS, but it can be corrected by the harmonic orbit correctors. (c) 2000 The American Physical Society.

It is required to have an uncontrolled beam loss less than 1 nA/m at 1 GeV energy for hands-on maintenance of the Spallation Neutron Source (SNS) Accumulator Ring. Collimators will be used for this end. Various beam dynamics questions related with the collimators have been studied. Various factors are optimized with the given ring lattice and error study is done. Numerical simulations also indicate that movable shielding is necessary for a few hot places downstream of the primary collimator. These simulations indicate that with properly designed collimators the uncontrolled beam-loss requirements of the SNS accumulator ring may be achievable.

Experimental observation of particle diffusion mechanism in the presence of overlapping parametric resonances generated by a time dependent rf phase modulation is analyzed. We find that the regime of fast emittance growth is associated with the rapid particle motion along the separatrix of a dominant parametric resonance, the slow growth regime is related to particle diffusion in the chaotic sea, and the emittance saturation occurs when beam particles fill the chaotic region bounded by an invariant torus. Experimental data observed at the Indiana University Cyclotron Facility (IUCF) Cooler Ring are shown to agree well with the theoretical analysis. {copyright} {ital 1998} {ital The American Physical Society}

The compact finite difference method was developed for calculating the off median plane magnetic field components of cyclotrons when only the measured midplane field data are available. It has been shown that the proposed compact finite difference differentiators are better than the finite difference differentiators previously reported by the author. The proposed compact finite difference method was tested by comparing the frequency response, by applying to an analytical magnetic field, and by applying to measured magnetic field data of the K1200 superconducting cyclotron at the National Superconducting Cyclotron Laboratory. It should be pointed out that this improvement was obtained at the expense of more complicated machinery of mathematics, namely solving matrix problems.

We investigate effects of quantum fluctuation, potential well distortion, quantum lifetime, and Touschek lifetime of the quasi-isochronous (QI) dynamical system. The Fokker-Planck equation is employed to study the equilibrium bunch distribution. The quantum lifetime in the moderate damping regime is compared with analytical formulae. The effects of harmonic radio-frequency phase modulation on equilibrium distribution function, quantum lifetime reduction, and the occurrence of stochastic resonance are studied. The formula for the Touschek lifetime for the QI dynamical system is derived and studied.

The synchrotron equation of motion in quasi-isochronous ~QI! storage rings is transformed to a universal Weierstrass equation, where the solution is given by Jacobian elliptic functions. Scaling properties of the QI Hamiltonian are derived. The effects of phase space damping and the sensitivity of particle motion to external harmonic modulation are studied. We find that the rf phase modulation is particularly enhanced in QI storage rings. Exact formula and sum rules for resonance strength coefficients are derived. When the QI dynamical system is subject to harmonic modulation, it exhibits a sequence of period-2 bifurcations leading to global chaos in a region of modulation tune. This means that the operators of QI storage rings should pay special attention to rf phase noise. @S1063-651X~96!06707-4#

Given a magnet with midplane symmetry, the field is totally determined if one knows the field in the midplane. A new finite difference method for calculating the field from discrete data in the midplane is described. Because data to be processed are obtained from measurements with noise, the method for evaluating derivatives is required to suppress the high frequency signals effectively, while maintaining reasonable accuracy for low frequencies. First-order and second-order differentiators for a uniform mesh are designed. As a test, they are applied to the magnetic field produced by two magnetized iron bars where the exact analytical expression for the magnetic field is known and also they are applied to the same field data when a small amount of noise is superimposed. And, finally, they are applied to the measured magnetic field of the K1200 super conducting cyclotron.

The fourth-order resonance ν z = 3 4 often occurs in the pre-extraction region of three-sector superconducting cyclotrons, and acceleration through this resonance can deform the vertical (and radial) phase space of the beam. The phase-space properties near the resonance have been explored using an improved version of the Z 4 Orbit Code and magnetic field data from the K1200 superconducting cyclotron at this laboratory. The orbit code results have been compared with those obtained from a standard theoretical analysis based on an expansion of the Hamiltonian. This comparison shows that relatively good agreement can be obtained if and only if certain third-order coupling effects are included in the theory. These effects are associated with particular coupling resonances that are not very far from the operating point.

In a particle accelerator with a periodic structure beam space charge force may excite resonant beam emittance growth if the particle's transverse phase advance approaches 90\ifmmode^\circ\else\textdegree\fi{}. A recent simulation study with the PARMILA code [D. Jeon et al., Phys. Rev. ST Accel. Beams 12, 054204 (2009)] has shown the feasibility of measuring the stop band of this fourth order resonance in the GSI Universal Linear Accelerator UNILAC and proposed its experimental verification, which is reported here. Measurements of transverse phase space distributions behind a periodically focusing structure reveal a fourfold symmetry characteristic of fourth order resonances as well as a resonance stop band above ${\ensuremath{\sigma}}_{0}=90\ifmmode^\circ\else\textdegree\fi{}$ per focusing cell. These experimental findings agree with results from three different beam dynamics simulation codes, i.e., DYNAMION, PARMILA, and TRACEWIN.

Using improved techniques, analytical formulas are derived for calculating the orbit period, the radial tune, and the vertical tune as a function of energy for a given magnetic field. As examples, these formulas are applied to fields from two different machines: the three-sector K1200 superconducting cyclotron at this laboratory, and the six-sector 500 MeV cyclotron at the TRIUMF laboratory. A comparison of the results with those from a standard orbit integration program shows that the analytical formulas are, on the average, highly accurate for the orbit period, quite accurate for the radial tune, but only moderately accurate for the vertical tune. Moreover, differences between the theoretical and orbit code results are found to exhibit relatively large fluctuations which are produced by small irregularities in the measured field data.

Physical review accelerators and beams 11(9), 094201(2008). doi:10.1103/PhysRevSTAB.11.094201, Published by American Physical Society, College Park, MD

The Spallation Neutron Source accelerator systems will deliver a 1.0 GeV, 1.4 MW proton beam to a liquid mercury target for neutron scattering research. The accelerator complex consists of an H-injector, capable of producing one-ms-long pulses at 60 Hz repetition rate with 38 mA peak current, a 1 GeV linear accelerator, an accumulator ring and associated transport lines. The 2.5 MeV beam from the Front End is accelerated to 86 MeV in the Drift Tube Linac, then to 185 MeV in a Coupled-Cavity Linac and finally to 1 GeV in the Superconducting Linac. With the completion of beam commissioning, the accelerator complex began operation in June 2006 and beam power is being gradually ramped up toward the design goal. Operational experience with the injector and linac will be presented including chopper performance, transverse emittance evolution along the linac, and the results of a beam loss study.

The GSI UNILAC, a heavy ion linac originally dedicated for low current beam operation, together with the synchrotron SIS 18 will serve as a high current injector for FAIR (international facility for antiproton and ion research). The UNILAC post stripper accelerator consists of five Alvarez tanks with a final energy of 11.4 MeV/u. In order to meet the requirements of FAIR 15 emA 238U28+, transverse normalised emittances of 0.8 m mrad and 2.5 mm mrad an UNILAC upgrade program is foreseen to increase the primary beam intensity as well as the beam brilliance. A detailed understanding of the beam dynamics during acceleration and the transport of space charge dominated beams is necessary. For this purpose the beam brilliance dependency on the phase advances in the Alvarez DTL was studied. Machine investigations were performed with various beam diagnostics devices established in the UNILAC. Measurements done in 2006 using a high intensity heavy ion beam coincide with the beam dynamics work package of the European JRA "high intensity pulsed proton injector" (HIPPI). Results of these measurements are presented as well as corresponding beam dynamics simulations.

The Spallation Neutron Source accelerator systems will provide a 1 GeV, 1.44 MW proton beam to a liquid mercury target for neutron production. The accelerator complex consists of an H-injector capable of producing 38 mA peak current, a 1 GeV linear accelerator, an accumulator ring and associated transport lines. The linear accelerator consists of a Drift Tube Linac, a Coupled-Cavity Linac and a Superconducting Linac which provide 1.5 mA average current to the accumulator ring. The staged beam commissioning of the accelerator complex is proceeding as component installation progresses. Recently, the normal-conducting linear accelerator was beam commissioned. A number of beam dynamics and beam quality measurements will be reported, including the measurement of transverse emittances in the H-injector, and the evolution of halo and emittance along the linac.

An automated transverse beam matching application has been developed for the Spallation Neutron Source (SNS) beam transport lines. The application is written within the XAL Java framework and the matching algorithm is based on the simplex optimization method. Other functionalities, such as emittance calculated from profile monitor measurements (adopted from a LANL Fortran code), profile monitor display, and XAL on-line model calculation, are also provided by the application. Test results obtained during the SNS warm linac commissioning will be reported. A comparison between the emittances obtained from this application and an independent Trace-3D routine will also be shown.